Does Goldman have a better economic pulse than BofA?

FORTUNE – In the biggest change of the 30-stock index in nearly a decade, three companies will be replaced on the Dow Jones Industrial Average. Alcoa, Bank of America, and Hewlett-Packard are out, Nike, Goldman Sachs, and Visa V are in.

The shake-up partly reflects declining fortunes and share prices, but the timing and reasons are nonetheless curious when we look at the departure of Bank of America BAC. Like other big banks, the Charlotte, N.C.-based bank lost big from the subprime mortgage market meltdown, and it’s hard not to wonder why the Dow didn’t delist the bank when it was losing billions of dollars and had the government swoop into the rescue.

The Dow gave Citigroup C the boot in 2009 while it was recovering from its own taxpayer-funded bailout following the financial crisis. Like Bank of America, it is steadily coming back — Citi is trading at about $50 a share today, roughly where Bank of America was in 2007.

To be sure, the Dow INDU is a price-weighted index. So unlike the closely watched Standard & Poor’s 500-stock index SPX, which is weighted by market capitalization or essentially a company’s size, the Dow is driven largely by stock prices. Today, Bank of America is trading at about $14 a share as it continues its road to recovery largely by cutting costs. Next to Alcoa AA, Bank of America had the second-lowest stock in the index. But it was up from $5 at the end of 2011.

The index changes, however, go beyond stock prices. In delisting Bank of America, the Dow also wanted to include a more diverse mix of companies in the index. The goal is to more accurately capture the pulse of the broader economy.

“When you only have 30 positions to fill you have to make sure every position pays off,” says David Blitzer, managing director and chairman of S&P’s index committee. He adds that JPMorgan Chase JPM, among the 30 companies listed in the Dow, runs a similar business as Bank of America.

“Goldman is different from Bank of America,” Blitzer adds. It’s an investment bank.

Different? Or better? Regardless, that doesn’t explain how Goldman GS acts as a better pulse of America’s economy than Bank of America, the nation’s second-largest bank. Goldman might say a lot about what’s happening on Wall Street, but Bank of America says a lot about how average Americans are doing — perhaps more so today and in the coming years than previous years. CEO Brian Moynihan has vowed to pull back from risk, selling off mortgage-servicing rights and private-equity investments and instead focusing on more consumer-focused banking products, such as credit cards, home loans, and checking accounts.

Whatever is driving the changes, the index is in for smaller moves. Currently a $1 rise or fall in companies listed on the Dow moves the index 7.68 points. With all the changes, the same $1 move is expected to move the index 6.49 points, according to analysts at Birinyi Associates in a report to clients Tuesday.

This perhaps isn’t shocking, as a chunk of America will be left out of the Dow.